CN112800641A - Generalized coarse net finite difference acceleration method based on region decomposition parallel - Google Patents

Generalized coarse net finite difference acceleration method based on region decomposition parallel Download PDF

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CN112800641A
CN112800641A CN202011518814.6A CN202011518814A CN112800641A CN 112800641 A CN112800641 A CN 112800641A CN 202011518814 A CN202011518814 A CN 202011518814A CN 112800641 A CN112800641 A CN 112800641A
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徐飞
吴文斌
明平洲
赵晨
罗琦
姚栋
于颖锐
柴晓明
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Nuclear Power Institute of China
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Abstract

The invention discloses a generalized coarse net finite difference acceleration method based on area decomposition parallel, which comprises the following steps: s1, constructing a reactor core geometric object and a sub-region geometric object according to the geometric discrete information in the grid file; constructing a two-stage grid structure according to the geometric object of the reactor core, and merging each independent fine grid into a coarse grid by taking the specific parameters of the reactor core as merging rules; constructing a set mapping relation between the fine grids and the coarse grids; s2, cutting the long characteristic line according to the reactor core geometric object, and performing fine-mesh tracking on the cut characteristic line to generate characteristic line segment information for transportation and scanning; s3, determining the coarse grid adjacent condition in each sub-area and the coarse grid adjacent condition between the sub-areas according to the long characteristic line area decomposition tracking information; and S4, obtaining the fine grid flux based on the MOC source iterative solution, and introducing GCMFD acceleration. The method solves the problem that the existing generalized coarse net finite difference method cannot be applied to large-scale reactor core calculation.

Description

Generalized coarse net finite difference acceleration method based on region decomposition parallel
Technical Field
The invention relates to the field of nuclear reactor core design and reactor physical numerical calculation, in particular to a generalized coarse mesh finite difference acceleration method based on regional decomposition parallelism.
Background
In recent years, a 2D/1D coupling Method has become one of the mainstream methods for high-fidelity and fine-definition neutron calculation of a whole core, and the key of the Method is radial two-dimensional Characteristic line (MOC) calculation. The MOC method has the advantages of high calculation precision, good geometric adaptability, capability of accurately processing anisotropic scattering, multiple parallel dimensions and the like, however, the whole stack coupling in the scanning solving process of the MOC method is weak, the convergence speed is low, and an effective acceleration method is required.
Scholars at home and abroad develop a great deal of research aiming at the transportation acceleration method. Based on the basic ideas of low-order acceleration high-order, coarse-net acceleration fine-net, diffusion acceleration transportation, few-group acceleration multi-group and the like, the acceleration method can be mainly divided into two types, namely a comprehensive acceleration method based on linear correction and a rebalancing method based on nonlinear correction. The former includes a double spherical harmonic function expansion comprehensive acceleration, a transportation comprehensive acceleration method, an algebraic compression acceleration method and the like, and the latter includes a coarse network rebalancing method, a generalized coarse network rebalancing method, a coarse network finite difference method, a generalized coarse network finite difference method, an angle-dependent rebalancing acceleration method, a self-collision rebalancing acceleration method and the like. Among the above acceleration methods, the Coarse Mesh Finite Difference method (CMFD) couples the spatial grid and the inter-energy-group effect, has a good acceleration effect, can also adapt to large-scale parallel computation (for example, spatial region decomposition parallel), and is currently widely applied to two-dimensional MOC computation of most reactor cores. However, the CMFD method can only be based on a regular coarse grid, and limits the MOC arbitrary geometric adaptability to a certain extent.
The scholars propose a Generalized Coarse Mesh Finite Difference (GCMFD) method on the basis of the CMFD method. The method can utilize irregular coarse grids to perform coarse grid accelerated calculation, has strong geometric adaptability, is most suitable for convergence acceleration of MOC (metal oxide semiconductor) solution with complex geometry, but is not suitable for large-scale parallel calculation in the prior application, is limited by the calculated amount and storage amount of a complete set of geometric information, and has small solving application scale.
Disclosure of Invention
The invention aims to provide a generalized coarse net finite difference acceleration method based on region decomposition parallel, and solves the problem that the existing generalized coarse net finite difference method cannot be applied to large-scale reactor core calculation.
The invention is realized by the following technical scheme:
a finite difference acceleration method of a generalized coarse network based on region decomposition parallel comprises the following steps:
s1, constructing a grid structure:
s11, constructing a reactor core geometric object and a sub-region geometric object according to the geometric discrete information in the grid file;
s12, constructing a grid structure based on the reactor core geometric objects, wherein the grid structure comprises a first-level grid and a second-level grid, the first-level grid is composed of a plurality of second-level grids, the second-level grid is composed of a plurality of fine grids, each independent fine grid is combined into a coarse grid by taking the specific parameters of the reactor core as combination rules, and each sub-region comprises a plurality of coarse grids;
s13, establishing a solving area in the first-level grid according to the reactor core geometric objects, wherein the boundaries of the reactor core geometric objects are arranged in the solving area, and the solving area is of a regular rectangular structure; constructing a set mapping relation of the fine grids and the coarse grids in each sub-region;
s2, arranging long characteristic lines: cutting the long characteristic line according to the reactor core geometric object, and performing fine-mesh tracking on the cut characteristic line according to the sub-region geometric object to generate characteristic line segment information for reactor core neutron transport scanning;
s3, determining the coarse grid adjacent condition in each sub-area and the coarse grid adjacent condition between the sub-areas according to the long characteristic line area decomposition tracking information;
and S4, obtaining the fine grid flux based on MOC source iterative solution, and introducing GCMFD acceleration in the source iterative solution process.
At present, most of the two-dimensional MOC calculation of the reactor core adopts a coarse mesh acceleration method based on a rule, and the GCMFD method can perform coarse mesh acceleration calculation by using an irregular coarse mesh, so that the method has strong geometric adaptability, but is limited by the calculated amount and the storage amount of a whole set of geometric information, and the solving application scale is small.
The grid file is a known engineering file or an engineering file which can be obtained by a person skilled in the art, and is generated by graphical modeling software for describing the geometric information of the discrete grid; the sub-region geometric objects may be divided according to core assembly geometric objects.
The grid structure constructed by the invention is a two-stage grid structure and comprises a first-stage grid and a second-stage grid, wherein the first-stage grid is composed of a plurality of second-stage grids, the second-stage grid is composed of a plurality of fine grids, each independent fine grid is merged into a coarse grid by taking specific parameters of a reactor core as merging rules, each sub-region comprises a plurality of coarse grids, an 'equivalent' neutron diffusion problem is constructed by calculating equivalent homogenization parameters of the coarse grids, the adjacent condition of the coarse grids in each sub-region and the adjacent condition of the coarse grids between the sub-regions are determined by utilizing long characteristic line region decomposition tracking information, and GCMFD acceleration is introduced in the source iteration solving process, so that the transport calculation convergence is accelerated.
The method comprehensively considers coarse net calculation and two-stage grid area decomposition, and can carry out multi-process parallel construction and solution on the reactor core coarse net diffusion equation set under the conditions of irregular subregion division and coarse grid division, thereby realizing convergence acceleration of MOC transport parallel solution of the complex geometric reactor core, solving the problem that the conventional GCMFD acceleration method is limited in application scale, and being suitable for large-scale reactor core calculation.
Further, the set mapping relationship between the fine mesh and the coarse mesh is to merge a plurality of fine meshes into a coarse mesh, and the shape of the coarse mesh is a regular or irregular rectangle or polygon.
Further, the coarse mesh division is based on the form of the coarse mesh coefficient matrix.
Further, the sub-regions are divided into arbitrary regular and/or irregular polygons.
Further, sub-area partitioning is referenced to load balancing and bounded traffic.
Further, the first-level mesh is in the form of a regular or irregular rectangular arrangement, or a regular or irregular polygonal arrangement.
Further, the specific parameters of the core in step S12 include single connected regions of cells or other reasonable shapes.
Further, the specific process of step S4 is as follows:
s41, performing MOC solution source iteration, calculating the flux of the fine grids, and counting neutron net flow between the coarse grids in the characteristic line scanning process;
s42, calculating the effective value-added coefficient k by adopting a GCMFD moduleeff；
S43, judging flux distribution and k of the fine grideffWhether to converge; if the convergence exists, the program is ended, otherwise, the next MOC source iteration is continued.
Further, the specific process of step S42 is as follows:
obtaining a coarse grid homogenization parameter according to the conservation of the reaction rate, then calculating a coupling coefficient between the coarse grids by using the homogenization parameter and neutron net flow obtained by characteristic line scanning, further constructing a GCMFD equation set, obtaining new coarse grid flux through source iteration solution, and then correcting the fine grid flux.
Further, the characteristic line tracking task and the scanning solving task of each sub-region are distributed to a plurality of MPI processes to be executed in parallel by adopting an MPI programming model, then each MPI process respectively calculates the coarse network parameters in the corresponding sub-region and constructs a corresponding partial GCMFD equation set, a mathematical base parallel solver is used for solving the whole equation set, and the fine network flux correction in the corresponding sub-region is respectively executed after a plurality of iterations of the GCMFD source.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the method can carry out multi-process parallel construction and solution on the reactor core coarse mesh diffusion equation set under the conditions of irregular subregion division and coarse grid division, thereby realizing convergence acceleration of MOC transport parallel solution of the complex geometric reactor core, solving the problem that the conventional GCMFD acceleration method is limited in application scale and being suitable for large-scale reactor core calculation.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flowchart of the calculation of the GCMFD accelerated MOC;
FIG. 2 is a schematic diagram of two-level mesh and coarse mesh partitioning;
FIG. 3 is a schematic diagram of a coefficient matrix of the GCMFD equation set (16 cells, 2 energy groups, 4 subregions).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1:
as shown in fig. 2 and fig. 3, a generalized coarse-mesh finite difference acceleration method based on region decomposition parallel includes the following steps:
s1, constructing a grid structure:
s11, constructing a reactor core geometric object and a sub-region geometric object according to the geometric discrete information in the grid file;
s12, constructing a grid structure based on the reactor core geometric objects, wherein the grid structure comprises a first-level grid and a second-level grid, the first-level grid is composed of a plurality of second-level grids, the second-level grid is composed of a plurality of fine grids, each independent fine grid is combined into a coarse grid by taking the specific parameters of the reactor core as combination rules, the coarse grid division takes the form of a coarse grid coefficient matrix as reference, the coarse grid is in a regular or irregular rectangular or polygonal shape, each sub-region comprises a plurality of coarse grids, and the first-level grid is in a regular or irregular rectangular arrangement or in a regular or irregular polygonal arrangement;
s13, establishing a solving area in the first-level grid according to the reactor core geometric objects, wherein the boundaries of the reactor core geometric objects are arranged in the solving area, and the solving area is of a regular rectangular structure; constructing a set mapping relation of the fine grids and the coarse grids in each sub-region;
s2, arranging long characteristic lines: cutting the long characteristic line according to the reactor core geometric object, and performing fine-mesh tracking on the cut characteristic line according to the sub-region geometric object to generate characteristic line segment information for reactor core neutron transport scanning;
s3, determining the coarse grid adjacent condition in each sub-area and the coarse grid adjacent condition between the sub-areas according to the long characteristic line area decomposition tracking information;
s4, obtaining fine grid flux based on MOC source iterative solution, and introducing GCMFD acceleration in the source iterative solution process:
s41, performing MOC solution source iteration, calculating the flux of the fine grids, and counting neutron net flow between the coarse grids in the characteristic line scanning process;
s42, calculating the effective value-added coefficient k by adopting a GCMFD moduleeff；
Specifically, the method comprises the following steps:
acquiring a coarse grid homogenization parameter according to the conservation of the reaction rate, calculating a coupling coefficient between coarse grids by using the homogenization parameter and neutron net flow obtained by characteristic line scanning, further constructing a GCMFD equation set, obtaining new coarse grid flux through source iteration solution, and then correcting the fine grid flux;
s43, distributing the characteristic line tracking task and the scanning solving task of each sub-area to a plurality of MPs by adopting the MPI programming modelThe I processes are executed in parallel, then each MPI process respectively calculates the coarse network parameters in the corresponding sub-area and constructs a corresponding partial GCMFD equation set, a mathematical library parallel solver is called to solve the whole equation set, and fine network flux correction in the corresponding sub-area is respectively executed after a plurality of iterations of the GCMFD source; determining fine-grid flux distribution and keffWhether to converge; if the convergence exists, the program is ended, otherwise, the next MOC source iteration is continued.
The working principle and the calculation process of the embodiment are as follows:
MOC transport calculation generally divides different material areas into finer grids, coarse grid finite difference (CMFD) acceleration calculation combines the fine grids into coarse grids according to certain requirements, an 'equivalent' neutron diffusion problem is constructed by calculating equivalent homogenization parameters of the coarse grids, a coarse grid coupling correction factor is introduced, and the neutron diffusion problem is rapidly solved by utilizing a finite difference format. The results from the coarse net diffusion calculations, while not really convergent to the problem understanding, are macroscopically closer to the true flux distribution and are used to correct the results from the fine net transport calculations to speed convergence. In the process of acceleration calculation, the flux of the fine grid is solved through transport calculation, input parameters are provided for coarse grid calculation, the flux of the coarse grid is obtained through solving a coarse grid multi-group diffusion equation set, then nonlinear correction is carried out on the flux of the fine grid, and the alternate iterative solution is carried out until convergence is achieved.
Integrating a neutron transport equation in a 4 pi angle space, and integrating a coarse grid i under a two-dimensional condition to obtain the result after simplification:
Figure RE-GDA0002996995490000051
in the formula, Si,SIs the equivalent length of the coarse mesh i at the boundary,
Figure RE-GDA0002996995490000052
defining the direction of the coarse grid i flowing to the outside of the boundary as a positive direction for g groups of net neutron flows of the coarse grid i at the boundary; j denotes the phase i with the coarse gridAdjacent grid numbering, Si,jRepresenting the equivalent length of the interface between coarse meshes i and j,
Figure RE-GDA0002996995490000053
defining the direction of the net neutron flow of the g group between the coarse grids i and j from the coarse grid i to the coarse grid j as a positive direction; viIs the area of the coarse grid i,
Figure RE-GDA0002996995490000054
is the g group scalar flux for the coarse grid i,
Figure RE-GDA0002996995490000055
is the total cross-section of the group g of the coarse grid i,
Figure RE-GDA0002996995490000056
the g cluster total source entries for the coarse grid i.
The net flow of neutrons in the interface is assumed to be calculated as follows:
Figure RE-GDA0002996995490000057
Figure RE-GDA0002996995490000058
wherein the content of the first and second substances,
Figure RE-GDA0002996995490000059
and
Figure RE-GDA00029969954900000510
for the coupling coefficient between the coarse meshes i and j,
Figure RE-GDA00029969954900000511
is the coefficient of the coarse grid i at the boundary.
According to the formulas (1) to (3), a coarse mesh multi-group diffusion equation system can be obtained:
Figure RE-GDA00029969954900000512
finite difference discrete format, coupling coefficient according to Fick's law
Figure RE-GDA0002996995490000061
The expression of (a) is:
Figure RE-GDA0002996995490000062
in the formula, hiAnd hjThe widths of the grids i and j respectively,
Figure RE-GDA0002996995490000063
and
Figure RE-GDA0002996995490000064
the g group diffusion coefficients for grids i and j, respectively.
For irregular grids, coupling coefficients cannot be obtained through discretization by using a finite difference method
Figure RE-GDA0002996995490000065
The expression of (2), i.e., (5), no longer applies, and then the generalized coarse mesh finite difference method (GCMFD) is used to process the irregular coarse mesh. In the two-dimensional case, the coupling coefficient in the GCMFD method
Figure RE-GDA0002996995490000066
The calculation expression of (a) is as follows:
Figure RE-GDA0002996995490000067
Figure RE-GDA0002996995490000068
in the formula (I), the compound is shown in the specification,
Figure RE-GDA0002996995490000069
is the equivalent width, V, of the irregular coarse grid iiFor the area of the coarse grid i, ρ is the equivalent width factor (default set to 0.6 in the present invention).
For general coarse grid geometry, the interface equivalent length S between adjacent coarse gridsi,jThe solving formula of (2) is as follows:
Figure RE-GDA00029969954900000610
wherein m is the azimuth number, K is the characteristic line number, KmRepresents the set of all the characteristic lines in the m direction passing through the coarse grids i and j in sequence, Δ dkRepresenting the width of the characteristic line k. Under different azimuth angles, the sum of the widths of the characteristic lines successively passing through the coarse grids i and j is different, and the maximum value in all the azimuth angle conditions is defined as the interface equivalent length S of the coarse grids i and ji,j. And (3) aiming at the MOC transportation calculation of the region decomposition parallel, the complex adjacent relation of the irregular coarse grid of the reactor core is obtained by utilizing the long characteristic line region decomposition parallel tracking information.
Net flow of neutrons between coarse grids
Figure RE-GDA00029969954900000611
The solving formula of (2) is as follows:
Figure RE-GDA00029969954900000612
Figure RE-GDA00029969954900000613
in the formula, ωnFor polar angle integration group, omegamFor the set of the quadrature of the azimuth angles,
Figure RE-GDA00029969954900000614
g group for emitting n polar angle m azimuth angle k-th characteristic line obtained by MOC transportation calculation from coarse grid i to coarse grid jNeutron angular flux.
Net flow of neutrons at the boundary
Figure RE-GDA00029969954900000615
Figure RE-GDA00029969954900000616
In the formula (I), the compound is shown in the specification,
Figure RE-GDA0002996995490000071
and g-group neutron angular flux is emitted from the coarse grid i to the vacuum boundary from the k-th characteristic line of the n polar angle m azimuth angle obtained by MOC transport calculation.
The GCMFD equation system is constructed for all the coarse grids of the whole reactor core, and the construction and the solution are based on multi-process parallel. In order to describe the construction and solving process of the coefficient matrix of the equation set more intuitively, a simple 4 × 4 cell is taken as an example (2 energy group, 4 sub-region, total reflection boundary), as shown in fig. 1. If the grid is divided into one coarse grid according to one cell, the example contains 16 coarse grids (each sub-region contains 4 coarse grids), and the coarse grid coefficient matrix is 32 × 32. In the process of constructing the coefficient matrix, each process separately constructs and stores a partial matrix corresponding to a sub-region, i.e. a 8 × 32 strip-shaped sub-matrix in the corresponding graph. The sub-region division and the coarse mesh division can be any irregular polygon, but in practical application, the sub-region division needs to consider load balance and the communication traffic of a boundary, and the coarse mesh division needs to consider the form of a coarse mesh coefficient matrix (for example, a coarse mesh in a slender shape is more likely to cause a sick coefficient matrix, and numerical solution is unstable, so the ratio of the perimeter to the area of the coarse mesh cannot be too large). And after respectively constructing corresponding partial coefficient matrixes and right-end source items, each process synchronously calls a parallel solver function interface to solve the coarse network equation set in parallel.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A finite difference acceleration method of a generalized coarse network based on region decomposition parallel is characterized by comprising the following steps:
s1, constructing a grid structure:
s11, constructing a reactor core geometric object and a sub-region geometric object according to the geometric discrete information in the grid file;
s12, constructing a grid structure based on the reactor core geometric objects, wherein the grid structure comprises a first-level grid and a second-level grid, the first-level grid is composed of a plurality of second-level grids, the second-level grid is composed of a plurality of fine grids, each independent fine grid is combined into a coarse grid by taking the specific parameters of the reactor core as combination rules, and each sub-region comprises a plurality of coarse grids;
s13, establishing a solving area in the first-level grid according to the reactor core geometric objects, wherein the boundaries of the reactor core geometric objects are arranged in the solving area, and the solving area is of a regular rectangular structure; constructing a set mapping relation of the fine grids and the coarse grids in each sub-region;
s2, arranging long characteristic lines: cutting the long characteristic line according to the reactor core geometric object, and performing fine-mesh tracking on the cut characteristic line according to the sub-region geometric object to generate characteristic line segment information for reactor core neutron transport scanning;
s3, determining the coarse grid adjacent condition in each sub-area and the coarse grid adjacent condition between the sub-areas according to the long characteristic line area decomposition tracking information;
and S4, obtaining the fine grid flux based on MOC source iterative solution, and introducing GCMFD acceleration in the source iterative solution process.
2. The finite difference acceleration method of generalized coarse mesh based on region decomposition parallelism as claimed in claim 1, wherein the set mapping relationship between the fine mesh and the coarse mesh is to merge multiple fine meshes into the coarse mesh, and the shape of the coarse mesh is regular or irregular rectangle or polygon.
3. The finite difference acceleration method of generalized coarse mesh based on area decomposition parallel of claim 2, characterized in that the coarse mesh division is referenced to the form of coarse mesh coefficient matrix.
4. The finite difference acceleration method of generalized coarse net based on region decomposition parallel of claim 1, characterized in that the sub-regions are divided into arbitrary regular and/or irregular polygons.
5. The finite difference acceleration method of generalized coarse net based on area decomposition parallel of claim 4, characterized in that the sub-area division is based on load balance and boundary traffic.
6. The finite difference acceleration method of generalized coarse mesh based on region decomposition parallel as claimed in claim 1, wherein the first-stage mesh is in the form of regular or irregular rectangular arrangement or regular or irregular polygonal arrangement.
7. The finite difference acceleration method based on the regional decomposition parallel generalized coarse net is characterized in that the specific parameters of the core in the step S12 include grid cells.
8. The finite difference acceleration method of generalized coarse net based on region decomposition parallel of claim 1, wherein the specific process of step S4 is as follows:
s41, performing MOC solution source iteration, calculating the flux of the fine grids, and counting neutron net flow between the coarse grids in the characteristic line scanning process;
s42, calculating the effective value-added coefficient k by adopting a GCMFD moduleeff；
S43, judging flux distribution and k of the fine grideffWhether to converge; if the convergence exists, the program is ended, otherwise, the next MOC source iteration is continued.
9. The finite difference acceleration method of generalized coarse net based on region decomposition parallel of claim 8, wherein the specific process of step S42 is as follows:
obtaining a coarse grid homogenization parameter according to the conservation of the reaction rate, then calculating a coupling coefficient between the coarse grids by using the homogenization parameter and neutron net flow obtained by characteristic line scanning, further constructing a GCMFD equation set, obtaining new coarse grid flux through source iteration solution, and then correcting the fine grid flux.
10. The finite difference acceleration method of the generalized coarse network based on the area decomposition parallelism as claimed in claim 8, characterized in that the MPI programming model is adopted to distribute the characteristic line tracking task and the scanning solving task of each sub-area to a plurality of MPI processes for parallel execution, then each MPI process calculates the coarse network parameters in the corresponding sub-area and constructs the corresponding partial GCMFD equation set, the mathematical library parallel solver is invoked to solve the whole equation set, and after a plurality of iterations of GCMFD sources, the fine network flux correction in the corresponding sub-area is executed respectively.
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